The Big Picture
What have we been doing? Computer simulation is a method of performing experiments without costly hardware. To be in this business, you need to become a very good experimentalist. Always remember that your experiments are performed in virtual worlds where the physical laws may be close to those of the real world, but never really match. You’ve got to use your full training as an engineer to detect the differences in physical laws and understand their impact. Never trust the results of a computer simulation until you (or someone you know and trust) have thoroughly tested the relationship between the virtual and real worlds.
If you haven’t learned the skills already, spend time learning how to construct controlled experiments. One major advantage of computer simulations is that you have far more opportunities for highly controlled experiments than you do in the real world. During this process you will be applying basic scientific method:
1. Make careful observations of a system;
2. Make a hypothesis to explain those observations;
3. Design a test (or tests) for the hypothesis;
4. Perform the test;
5. Either confirm your hypothesis, or revise it (loop back to 2).
When designing a test, limit the changes you introduce into the system. In computer simulation, there is almost never an excuse for introducing more than one change at a time.
we’re talking about
science, I want to remind you of a broader definition. Science is a
discipline that we have built over millennia, to help us see what is
there, not what we want to see. When
properly used Computer
Simulation is a tool that can help us see what is really there. However, be cautious of your fundamental
nature. Do not except the results of a
computer simulation (or any other observation) because they are what
to see. Use all of your experience and
training to be certain that the results adequately reflect reality.
1. Determine appropriate mathematical model
2. Classification of partial differential equation
3. Transformation of mathematical model
4. Select grid pattern
5. Formation of finite difference equations
6. Solution algorithm
7. Perform auxiliary calculations
In theory, this is the end of my career as a college teacher. Since many of you will be considering this as a profession, I'd like to pass on some thoughts. One of the flaws in the university system is that it is too inbred. Countless generations pass of professors training students who immediately become professors. Before entering college teaching, go out and experience the broader professional world. Come back to the university and share that experience with your students. However, if you intend to come back, remember the adage “publish or perish.” You should have a goal of two papers a year in refereed journals during your time away from the university.
You should think about your motivation for becoming a university professor. If you enjoyed your research and see the university as a way to continue doing such research, there are better places to do research. Government laboratories and good industry research centers will give you far more opportunity to focus on research than you will have as a university professor. As a professor you are pulled in too many directions and don’t get the opportunity to become one with your research project. Another consideration is that university professors normally don’t do research, they manage research. This is an easy way to get low level management experience, but if you want to head down this path, you will normally find opportunities to manage better quality research teams elsewhere.
You should also understand the intensity of the profession before starting down the road. I have worked as staff and management in government labs, worked closely with industry researchers, and come up through the tenure track process as a university professor. I can tell you that the work environment at a university is far more brutal than that of the other two options. The rewards associated with teaching, and running your own small scale research operation come at a heavy price to your broader life.
One other aspect of the profession deserves comment. Much is made of “academic freedom.” However, my observation has been that if you behave responsibly towards your students and colleagues, your practical level of freedom is not significantly higher than found in other scientific and engineering professions. Your freedom is restricted by the need for projects with a useful learning content, and by the natural limits associated with sleep deprivation.
I’d like to close with some observations related to Mahaffy’s second law of human nature:
There is no obvious correlation between intelligence and wisdom.
Pursue wisdom as you move through life, but don’t mistake caution for wisdom. I commented on several occasions that you develop a successful record in research by going with the odds. However, you need to keep track of the odds. Something that on first glance appears to be the safest approach, may when you consider it carefully just be headed for a dead end. There are times when approaches that are popularly regarded as foolhardy have the best chance of success. There are times when you need to do something foolhardy to preserve your sanity. Learn to sort this all out and you are well on the path to wisdom.